On Brezis' First Open Problem: A Complete Solution
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866913727547179008 |
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| author | Sun, Liming Wei, Juncheng Yang, Wen |
| author_facet | Sun, Liming Wei, Juncheng Yang, Wen |
| contents | In 2023, H.\,Brezis published a list of his ``favorite open problems", which he described as challenges he had ``raised throughout his career and has resisted so far". We provide a complete resolution to the first one--Open Problem 1.1--in Brezis's favorite open problems list: the existence of solutions to the long-standing Brezis-Nirenberg problem on a three-dimensional ball. Furthermore, using the building blocks of Del Pino-Musso-Pacard-Pistoia sign-changing solutions to the Yamabe problem, we establish the existence of infinitely many sign-changing, nonradial solutions for the full range of the parameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06904 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Brezis' First Open Problem: A Complete Solution Sun, Liming Wei, Juncheng Yang, Wen Analysis of PDEs Differential Geometry In 2023, H.\,Brezis published a list of his ``favorite open problems", which he described as challenges he had ``raised throughout his career and has resisted so far". We provide a complete resolution to the first one--Open Problem 1.1--in Brezis's favorite open problems list: the existence of solutions to the long-standing Brezis-Nirenberg problem on a three-dimensional ball. Furthermore, using the building blocks of Del Pino-Musso-Pacard-Pistoia sign-changing solutions to the Yamabe problem, we establish the existence of infinitely many sign-changing, nonradial solutions for the full range of the parameter. |
| title | On Brezis' First Open Problem: A Complete Solution |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2503.06904 |